caterina cumino
Politecnico di Torino, Disma, Faculty Member
Research Interests: Architecture and Bachelor
We present a set of guided tours and educational workshops, where the halls of a magnificent baroque royal residence become classrooms and visitors are led to discover architectural shapes and to understand their geometry with the use of... more
We present a set of guided tours and educational workshops, where the halls of a magnificent baroque royal residence become classrooms and visitors are led to discover architectural shapes and to understand their geometry with the use of various origami modeling activities, rigorously supported by mathematics (descriptive geometry and basics in analytic and differential geometry).
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Research Interests: Mathematics and H
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ABSTRACT Some results about the analytic branches of an algebraic affine variety along a singular subvariety are proved, using the theory of henselian rings. Precisely, let X=Spec(A), with A a noetherian domain, and Y a closed irreducible... more
ABSTRACT Some results about the analytic branches of an algebraic affine variety along a singular subvariety are proved, using the theory of henselian rings. Precisely, let X=Spec(A), with A a noetherian domain, and Y a closed irreducible subvariety of X corresponding to the prime p of A. The first result is that the global branches of X along Y, which by definition are the minimal primes of the henselization of the couple (A,p), correspond to the connected components of p -1 (Y), where p:X ' →X is the normalization morphism. Moreover, there is an open subset U of X such that there is a natural canonical correspondence between the global branches of U along U∩Y and the branches of X at the generic point y of Y. A similar result is then proved for the geometric global branches of X along Y, i.e. the minimal primes of the strict henselization of the couple (A,p), replacing the branches of X in y with the geometric branches of X in y. Furthermore it is shown how to reconstruct the local rings of the branches at each point of a dense open subset of Y knowing the branches at the generic point y, under some conditions for the behaviour of X along Y. This result is finally extended to the general case, passing to a suitable étale covering of X. For closely related results proved with completely different topological techniques see the paper by G. Tedeschi, Boll. Unione Mat. Ital., VI. Ser., D, Algebra Geom. 4, No.1, 17-27 (1985; see the preceding review)].
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Modelli cartacei per la comprensione della forma architettonica: ricerca, progetto, sperimentazione e didattica in un dialogo tra geometria e rappresentazione | Paper models for the understanding of architectural shape: research, design, testing and teaching in a dialogue between Geometry and Rep...more
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We present a set of guided tours and educational workshops, where the halls of a magnificent baroque royal residence become classrooms and visitors are led to discover architectural shapes and to understand their geometry with the use of... more
We present a set of guided tours and educational workshops, where the halls of a magnificent baroque royal residence become classrooms and visitors are led to discover architectural shapes and to understand their geometry with the use of various origami modeling activities, rigorously supported by mathematics (descriptive geometry and basics in analytic and differential geometry).
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Representing an architectural shape, mediating design/formal/semantic needs, means respecting its specificity according to the purposes with which one operates; therefore, teaching how to represent an architectural shape is a complex... more
Representing an architectural shape, mediating design/formal/semantic needs, means respecting its specificity according to the purposes with which one operates; therefore, teaching how to represent an architectural shape is a complex operation, especially if this happens in the first year of the degree course in Architecture where the heterogeneity of students’ background requires a preliminary definition of a common language. Students are firstly introduced to theoretical geometries which underlie architectural shapes. So, they have to know the basis of Geometry (both Descriptive and Analytical) in order to proceed within these issues. This process requires to underline the two ‘souls’ of architectural shapes: the theoretical and the build one. Moreover, it also leads to investigate two different types of theoretical shapes: the one that lies behind the design idea and the other one which underlies the built. We propose teaching examples focused on reading architectural shapes as a...
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We propose a construction of 3D origami model of mansard roofs, using interactive approaches between Mathematics and Architecture, through the common language of Geometry.
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Our main purposes are the disclosure of certain basic topics of geometry to a broad audience with the aim of enabling people to read geometric shapes that surround us, both from a mathematical and architectural point of view. In the... more
Our main purposes are the disclosure of certain basic topics of geometry to a broad audience with the aim of enabling people to read geometric shapes that surround us, both from a mathematical and architectural point of view. In the events that we organize, we always leave ample margin to material testing, following the learn-by-doing philosophy. In particular we use origami as a medium to convey some knowledge about shapes. We present various examples addressed to different audiences.
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Some results about the analytic branches of an algebraic affine variety along a singular subvariety are proved, using the theory of henselian rings. Precisely, let X=Spec(A), with A a noetherian domain, and Y a closed irreducible... more
Some results about the analytic branches of an algebraic affine variety along a singular subvariety are proved, using the theory of henselian rings. Precisely, let X=Spec(A), with A a noetherian domain, and Y a closed irreducible subvariety of X corresponding to the prime p of A. The first result is that the global branches of X along Y, which by definition are the minimal primes of the henselization of the couple (A,p), correspond to the connected components of p -1 (Y), where p:X ' →X is the normalization morphism. Moreover, there is an open subset U of X such that there is a natural canonical correspondence between the global branches of U along U∩Y and the branches of X at the generic point y of Y. A similar result is then proved for the geometric global branches of X along Y, i.e. the minimal primes of the strict henselization of the couple (A,p), replacing the branches of X in y with the geometric branches of X in y. Furthermore it is shown how to reconstruct the local rin...
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Research Interests: Mathematics and Esculapio
We show an example of a lesson, tested with teen-agers and children, in which, by developing an idea of Albert E. Bosman, we propose an origami model to depict geometric forms in order to help learning of arithmetical topics such as... more
We show an example of a lesson, tested with teen-agers and children, in which, by developing an idea of Albert E. Bosman, we propose an origami model to depict geometric forms in order to help learning of arithmetical topics such as powers of natural numbers and their sum, and also the principle of induction, with a tactile, visual and motion experience.
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We present an innovative educational experience, introducing Mathematics and in particular geometry as tools for understanding architectural shapes. We design a set of guided tours for a cultural heritage context, the Royal Residence of... more
We present an innovative educational experience, introducing Mathematics and in particular geometry as tools for understanding architectural shapes. We design a set of guided tours for a cultural heritage context, the Royal Residence of Venaria, using the language of origami modeling as a medium to share spatial knowledge.
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This contribution focuses on paper models of architectural surfaces, in particular on some roofing systems describable by developable ones. Drawing on an interdisciplinary approach, between Architecture and Mathematics, potentialities and... more
This contribution focuses on paper models of architectural surfaces, in particular on some roofing systems describable by developable ones. Drawing on an interdisciplinary approach, between Architecture and Mathematics, potentialities and criticalities of these models in explicitly conveying Geometry are investigated, in relation to educational and communicative tasks, both when they are used in a direct, tangible way, and when the use is mediated by images generated by them (thus indirect); we discuss on the possibility for models and images to communicate their explicit and implicit Geometries. The main issue discussed is that a material or analytical description unequivocally allows to grasp all the peculiarities of geometrical shapes, while other representations are subject to critical selection of data and are therefore affected by subjective interpretations; similarly, the translation of the physical model into images is the result of choices which emphasize certain object pec...
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To make the geometrical cognitive process more interactive, we produced teaching aids (tangible models, graphic tablets) that help students in visualizing their geometrical-analytical investigations of the architectural artifacts and... more
To make the geometrical cognitive process more interactive, we produced teaching aids (tangible models, graphic tablets) that help students in visualizing their geometrical-analytical investigations of the architectural artifacts and enhance their spatial prefiguration and critical form-reading skills, three-dimensional thinking and geometrical reading of shapes. Then, we looked for a medium suitable to create simple three-dimensional models, not only observable, like virtual models, not only tangible, like physical models proposed in the design studios, but also dynamic, using multiple media and languages in the same training message. As an example, we present here an interdisciplinary lesson between Calculus and Architectural Drawing and Survey Laboratory about developable surfaces, experimented on first year students of the bachelor program in Architecture. The lesson is based on the use of a graphic tablet and some origami inspired models: it summarizes the geometric description of a pyramid and a cloister vault of equal height and equal orthographic projection on the horizontal plane. We saw that tackling the same topic in both teaching contexts is not a useless overlap, but a stimulus to compare different languages and methods. 2D and 3D paper models of artifacts—and of projective reduction from 3D to the plane—aid spatial intuition and the subtle exercise of controlling mental images which replace artifacts, turning 3D configurations into signifying images. Moreover, this experience stimulates reading and evaluation of the drawn geometry (ruled surfaces, projections, developments), increasing critical sense in reading the built environment.
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We present some remarks on the different communicative features of images generated by physical models for architecture, our study is part of an interdisciplinary research and educational project between Representation and Mathematics... more
We present some remarks on the different communicative features of images generated by physical models for architecture, our study is part of an interdisciplinary research and educational project between Representation and Mathematics (with focus on Geometry). In particular, our work frames the problem of direct and indirect use of physical models, with attention to the constituent and readable geometry in the origami model (especially in its meaning of means to represent the architectural form).
In the seventeenth century, Guarino Guarini, mathematician and architect, affirmed that architecture, a discipline that primarily deals with measures, relies on geometry: therefore, the architect needs to know at least its basic... more
In the seventeenth century, Guarino Guarini, mathematician and architect, affirmed that architecture, a discipline that primarily deals with measures, relies on geometry: therefore, the architect needs to know at least its basic principles. On behalf of Guarini’s words, we designed a set of interdisciplinary teaching experiences, between mathematics (via a calculus course) and drawing (via our Architectural Drawing and Survey Laboratory courses) that we proposed to first-year under graduate students studying for an Architecture degree. The tasks concern mathematical and representational issues about vaulted roofing systems and are based on the use of physical models in conjunction with digital tools, in order to make the cognitive geometric process more effective, thus following a consolidated tradition of both disciplines.
Research Interests: Architecture and Geometry
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Research Interests: Mathematics and H
Sunto Diamo due definizioni, una topologica e una algebrica, di ordine di un ramo globale di una varietà lungo una sottovarietà. Poi mostriamo che queste due definizioni coincidono. Infine confrontiamo questo ordine con gli ordini dei... more
Sunto Diamo due definizioni, una topologica e una algebrica, di ordine di un ramo globale di una varietà lungo una sottovarietà. Poi mostriamo che queste due definizioni coincidono. Infine confrontiamo questo ordine con gli ordini dei relativi rami locali.